CN115373139A - Method for generating adjustable and controllable photon hook by irregular micro-nano structure - Google Patents
Method for generating adjustable and controllable photon hook by irregular micro-nano structure Download PDFInfo
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Abstract
The invention discloses a method for generating a controllable photon hook by an irregular micro-nano structure, which comprises the following steps: s1, introducing a structural constraint function to describe an irregular part of a cross section of an irregular micro-nano structure, wherein a structural constraint function expression comprises n coefficients, and the irregular part is provided with m vertexes; s2, determining coordinate information of the m vertexes in a rectangular plane coordinate system, and solving a relational expression between the abscissa or ordinate of the m vertexes and the n coefficients; and S3, regulating and controlling the n coefficients by adjusting the abscissa or the ordinate of the m vertexes, so that the parameters of the photon hook are controlled. The structural constraint function provided by the invention can realize the direct control of the function coefficient on the photon hook parameter, namely, the expected photon hook form can be obtained by regulating and controlling the coefficient value of the structural constraint function.
Description
Technical Field
The invention relates to the field of light field regulation, in particular to a method for generating a controllable photon hook by an irregular micro-nano structure.
Background
The photon hook is a local bending light field in a sub-wavelength scale, shows an important application value in the fields of optical imaging, nano particle processing, cell control rods, nonlinear optics, integrated optics and the like by virtue of the excellent characteristics of the sub-diffraction limit full width at half maximum, the sub-wavelength scale curvature radius and the like, and provides possibility for breakthrough of the next generation of optical imaging and optical control technology. With the theoretical research of the photon hook generation mechanism and the popularization and deepening of related applications, the research of the photon hook with adjustable and controllable parameters according to actual needs has important scientific significance and practical application value.
The initially realized photon hooks are produced by plane wave irradiation onto dielectric particles consisting of cuboids and triangular prisms (Yue L, minin O V, wang Z, et al Photonic hook: a new curved light beam [ J ]. Optics Letters,2018,43 (4): 771-774.). The shape characteristics and the field distribution of the photon hook depend on the geometric shape of the adopted dielectric particles and the dielectric properties of the material, and the phase velocity and the light wave interference of the transmitted light in different areas in the particles are changed by destroying the symmetry of the original structure, so that the photon hook with the bending characteristic is generated. In order to achieve adjustability of the parameters of the photon hook, the solutions implemented by researchers can be divided into three categories. The first category of schemes is to utilize asymmetric incident light conditions. There have been research groups that have proposed photon hooks that can achieve bending by asymmetric incidence of a light beam on a particle (Feifeiwang, lianqing Liu, pengYu, et al, three-dimensional super-resolution morphology by near-field analyzed white-light interferometry [ J ]. Scientific Reports,2016,6,24703.). The irradiation range of the incident light beam on the dielectric particles is controlled to enable the incident area to have asymmetry, and therefore a bent photon hook is generated. The second approach is to exploit material asymmetry in the particles. There have been researches on photon hooks produced by microcolumns composed of two semicylinders of different materials, the bending angle of which can be flexibly adjusted by rotating the microcolumns around the central axis (Guoqiang Gu, liyang Shao, jun Song, et al. Photonic hooks from Janus microcylinders [ J ]. Optics Express,2019,27,37771-37780.). A third type of solution is to exploit structural asymmetry. Based on the specular reflection of the tilted mirrors, researchers have adjusted the bending angle of the photon hook by placing the mirrors behind the particles and adjusting the tilt of the mirrors (y.e. signs, a.a.zemlyanov, i.v. min, et al.spectral-reflection photo generation unit irradiation of a super-coherent electronic micropatterne [ J ]. Journal of Optics, 8978 zft 8978.). Meanwhile, researchers have proposed adding a metal baffle in front of the light incident surface of the ellipsoid structure to adjust the bending direction of the photon hook by controlling the shielding position of the metal baffle (c.liu, h.chung, o.v. min, et al.shaping photonic hook via-controlled attenuation of fine-sized graded-index micro-encapsulation [ J ]. Journal of Optics, 8978 zft 8978.). However, in many control schemes, all structures of the dielectric particles are almost regular structures, and the control requirement for photon hooks of the particles with irregular structures cannot be met, so how to realize the control of photon hooks formed by the particles with irregular structures becomes a problem to be solved at present.
For the regulation and control of photon hooks with more complex micro-nano structures, no systematic regulation and control scheme exists so far.
Disclosure of Invention
In order to solve the problems, the invention provides a method for generating a controllable photon hook by an irregular micro-nano structure, which introduces a structure constraint function into the structure definition of the irregular micro-nano structure, and determines the boundary of the irregular structure through parameters in the function, so that the length, the bending angle and the bending direction of the photon hook are regulated and controlled.
In order to realize the purpose of the invention, the following technical scheme is adopted:
a method for generating a controllable photon hook by an irregular micro-nano structure comprises the following steps:
s1, introducing a structural constraint function to describe an irregular part of an irregular micro-nano structure cross section, wherein a structural constraint function expression comprises n coefficients, and the irregular part is provided with m vertexes;
s2, determining coordinate information of the m vertexes in a rectangular plane coordinate system, and solving a relational expression between the abscissa or ordinate of the m vertexes and the n coefficients;
and S3, regulating and controlling the n coefficients by adjusting the abscissa or the ordinate of the m vertexes, so that the parameters of the photon hook are controlled.
Further, the irregular micro-nano structure is a micro-nano structure with an arc-shaped recess in the cross section, the arc-shaped recess is described by a structural constraint function, the structural constraint function is an asymmetric parabola-like function, and the expression is as follows:
x＝Ay 2 +By+C+Dxy (1)
wherein A, B, C, D is the coefficient of the structural constraint function;
let M, N, P denote three vertexes of the depression, and establish a plane rectangular coordinate system xoy with one point on the connecting line of MN as an origin O, and the intersection point of the depression and the x axis is P; m, N, P coordinates are (0,a), (0, -b), and (-c, 0), respectively, a, b, c are greater than 0;
and obtaining a relational expression between a, b and c and coefficients A, B and C, D, and regulating and controlling the coefficient A, B, C, D by adjusting the sizes of a, b and c.
Further, the relationship between a, b, c and coefficients A, B, C, D is:
C＝-c (4)
further, the parameters of the photon hook include a bending angle, a bending direction and an effective length.
The invention has the beneficial effects that:
1) The structural constraint function provided by the invention can realize the direct control of the function coefficient on the photon hook parameter, namely, the expected photon hook form can be obtained by regulating and controlling the coefficient value of the structural constraint function.
2) The structure constraint function provided by the invention realizes regulation and control of the irregular micro-nano structure, and if the type of the structure constraint function is changed, the control of any irregular micro-nano structure can be realized theoretically.
3) The method for generating the irregular micro-nano structure regulated by the structural constraint function is simple in theoretical realization, meanwhile, the concave micro-column is simple to process, the requirement of light field regulation on experimental equipment is not high, and compared with the conventional experimental generation method of the local curved light field, the method has no additional element and is easy to realize.
Drawings
FIG. 1 is a three-dimensional schematic diagram of an irregular micro-nano structure in the invention;
FIG. 2 is a schematic cross-sectional view of an irregular micro-nano structure in the invention;
FIG. 3 is a graph showing the results of experiments in which b and c are unchanged and a is changed;
wherein (a) is a graph of experimental results under a =0.25 condition; (b) is a graph of experimental results under a =1.83 condition; (c) is a graph of experimental results under a =3.42 condition; (d) is a graph of experimental results under a =5.00 condition;
FIG. 4 is a graph showing the results of an experiment in which a and c are unchanged and the value of b is changed;
wherein (a) is an experimental result diagram of b = -0.25; (b) is a graph of experimental results under the condition that b = -1.83; (c) is a graph of experimental results under the condition of b = -3.42; (d) is a graph of experimental results under the condition of b = -5.00;
FIG. 5 is a graph showing the results of the experiment in which a and b are unchanged and the value of c is changed;
wherein, (a) is an experimental result chart of c = -9.00; (b) is a graph of experimental results under the condition of c = -7.50; (c) is a graph of experimental results under the condition of c = -6.00; (d) is a graph of experimental results under the condition of c = -4.50;
FIG. 6 is a graph of the results of experiments in accordance with the present invention to vary the coefficient values of the structural constraint function;
wherein, (a) is an experimental result graph of changing the coefficient a; (B) is a graph of experimental results with a varying coefficient B; (C) is a graph of experimental results with varying coefficient C;
FIG. 7 is a graph of experimental results of different effective lengths and bend angles of a photonic hook according to the present invention;
wherein, (a) is an experimental result chart that the effective length of the photon hook is 7.55 lambda and the bending angle is 17 degrees; (b) The test result chart is that the effective length of the photon hook is 8.72 lambda, and the bending angle is 15 degrees; (c) Is an experimental result chart of the effective length of the photon hook being 5.96 lambda and the bending angle being-14 degrees; (d) The effective length of the photon hook almost reaches 11.90 lambda, and is an experimental result chart of three times of bending;
Detailed Description
The following embodiments are further illustrated in the following description:
a method for generating a controllable photon hook by an irregular micro-nano structure is disclosed, as shown in figure 1, the irregular micro-nano structure is a micro-column with an arc-shaped recess on the cross section; the arc-shaped recess is described by a structural constraint function, the structural constraint function is an asymmetric parabolic-like function, and the expression is as follows:
x＝Ay 2 +By+C+Dxy (1)
wherein A, B, C, D is the coefficient of the structural constraint function;
let M, N, P represent three concave vertexes, as shown in fig. 2, a planar rectangular coordinate system xoy is established with one point on the MN connecting line as the origin O, coordinates of M, N, P are (0,a), (0, -b) and (-c, 0), respectively, and a, b and c are all greater than 0; a. the relationship between b, c and coefficients A, B, C, D is expressed as the following equation:
C＝-c (4)
the coefficient A, B, C, D of the structural constraint function is regulated and controlled through the formulas (2) to (5), and the control of the parameters of the photon hook is realized.
The regulation of the parameters of the photon hook is further illustrated by the following examples:
example 1
The present embodiment provides a method of adjusting a photon hook by changing the M point. As shown in fig. 2, a TE plane wave with a wavelength λ of 632.8nm propagates in the negative y-axis direction and is incident perpendicularly on the concave micro-pillars in vacuum, wherein the cross-section of the micro-pillars has a radius of 7 λ and a refractive index of 1.5. Due to the deflection effect of the medium on incident light, photon hooks are formed on the shadow side of the concave micro-cylinder, and three characteristic parameters are defined: i is max L and alpha. Wherein the maximum electric field intensity of the photon hook is I max Boundary strength of I max V. ie. Along the main mode lobe of the photon hook, two end points of the electric field intensity reaching the boundary intensity are respectively defined as a starting point and an end point, and the effective length L is the projection distance of the photon hook from the starting point to the end point along the y axis. The bending angle of the photon hook is defined as α, and is specified to be positive when the photon hook is bent to the right, and negative otherwise.
In this embodiment, the lower intersection point N and the vertex P of the structural constraint function are fixed, and coordinates thereof are set to (0, -1.83) and (-9.00,0), and when the coordinate range of the upper intersection point M is (0,0.25), (0,1.83), (0,3.42) to (0,5.00) changed, the obtained results are respectively as shown in fig. 3 (a-d), in which curves represent functions. As is clear from the four two-dimensional light field patterns, as the coordinate of M is gradually increased from (0,0.25) to (0,5.00), the opening of the recess becomes larger and larger, the oscillation of the vacuum gas in the recess portion is correspondingly enhanced, and the photon hook becomes longer, wider and weaker in intensity. As the length of the photonic hook changes, the bending angle thereof also makes a negative bend, as shown in fig. 3 (c). And as the ordinate of the M point continues to increase, the photon hook may be bent for a plurality of times at a small angle, as shown in fig. 3 (d).
Therefore, it can be concluded through this embodiment that a negatively curved photon hook and a multiply curved photon hook can be generated with an increase in the opening in the recess caused by the upward movement of the point M, and the effective length of the photon hook can also be regularly adjusted.
Example 2
The present embodiment provides a method of adjusting the length and angle of the photon hook by changing the lower intersection point N. The incident light field and medium conditions were the same as in example 1, and as shown in fig. 4 (a-d), the upper intersection point M (0,1.83) and the vertex P (-9.00,0) were fixed, and when the coordinates of N were (0, -0.25), (0, -1.83), (0, -3.42) and (0, -5.00), as the ordinate of N was decreased from-0.25 to-5.00, i.e., the opening of the depression was increased, the effective length of the photon hook was increased, the intensity distribution was decreased while being more uniform, and the oscillation inside the depression was decreased. And when the recess opening is small, the photonic hook has a large bending angle as shown in fig. 4 (b).
Therefore, it can be concluded from the present embodiment that, under the optical field condition, when the size of the lower opening of the micro-cylinder recess is properly increased, the effective length of the photon hook is increased and the light intensity distribution is uniform, which has good properties. Meanwhile, a smaller opening angle of the recess is more favorable for forming a larger bending angle by the photon hook.
Example 3
The present embodiment provides a method of adjusting the length and angle of the photon hook by changing the position of the vertex P. The conditions of the incident light field and the medium were the same as in example 1, as shown in FIG. 5. When the coordinates of P are (-9.00,0), (-7.50,0), (-6.00,0) and (-4.50,0), the field intensity distributions are shown in FIGS. 5 (a-d), respectively. For convenience of description, a depression depth smaller than the radius of the micro cylinder is defined as a shallow depression depth, and a depression depth larger than the radius of the micro cylinder is defined as a deep depression depth. When the apex P is moved from inside to outside, as shown in fig. 5 (a-d), the bending direction of the photon hook changes from the positive direction (fig. 5 (a)) to the negative direction (fig. 5 (d)), and the effective length of the photon hook also becomes shorter by the long direction (fig. 5 (a)) (fig. 5 (d)), and almost no significant photon hook is formed in fig. 5 (b) and fig. 5 (c). These phenomena are the result of the change in the refractive index profile of the concave micropillars due to the difference in the depth of the depression, where the direction of the light transmitted from the backlight side of the micropillars is significantly deflected, and where the light beam is hardly deflected, so that the effective length of the photon hook in the case of a deep depression is longer.
It can be concluded from this embodiment that the position of point P controls the bending direction of the photon hook, and that the deep depression depth is advantageous for increasing the effective length of the photon hook.
Example 4
This embodiment provides a method for adjusting a photon hook by comprehensively considering coefficients of a structural constraint function in combination with embodiments 1 to 3. The relationship between each coefficient and the opening angle and the depression depth is shown in different colors in fig. 6, in which fig. 6 (a-C) visually shows a two-dimensional structural view of the depression of the microcolumn when the coefficients A, B and C are respectively changed.
The values of the coefficients A, B, C, D and a, b, and c corresponding to the plurality of dimples in fig. 6 (a) are shown in table 1, and it is found by analysis that the smaller the coefficient, the larger the opening angle of the dimple, and this indicates the opening angle of the coefficient a, which is a main determining function. And according to the regulation and control law of embodiment 2, the opening angle can be reduced by increasing the coefficient a, so that the bending angle of the photon hook is increased.
TABLE 1
| A | B | C | D |
| 1.00 | -2.00 | -9.00 | -0.22 |
| 5.00 | -2.00 | -9.00 | -0.22 |
| 15.00 | -2.00 | -9.00 | -0.22 |
| 45.00 | -2.00 | -9.00 | -0.22 |
| 100.00 | -2.00 | -9.00 | -0.22 |
| a | b | c | |
| 4.16 | -2.16 | 9.00 | |
| 1.56 | -1.16 | 9.00 | |
| 0.84 | -0.71 | 9.00 | |
| 0.47 | -0.43 | 9.00 | |
| 0.31 | -0.29 | 9.00 |
The values of coefficients A, B, C, D and a, B, c corresponding to the plurality of recesses in fig. 6 (B) are shown in table 2, and it is analytically known that the rotation direction of the function depends on the coefficient B, such that when the coefficient B > 0, the function curve rotates downward around the vertex as the coefficient B increases, and when the coefficient B < 0, the function curve rotates upward around the vertex as the coefficient B decreases. According to the regulation rule of example 2, the coefficient B controls the effective length of the photon hook, so that the coefficient B is greater than 0, and the photon hook with longer effective length can be obtained.
TABLE 2
| A | B | C | D |
| 5.00 | -20.00 | -9.00 | -2.22 |
| 5.00 | -10.00 | -9.00 | -1.11 |
| 5.00 | 0.00 | -9.00 | 0.00 |
| 5.00 | 10.00 | -9.00 | 1.11 |
| 5.00 | 20.00 | -9.00 | 2.22 |
| a | b | c | |
| 4.41 | -0.14 | 9.00 | |
| 2.67 | -0.67 | 9.00 | |
| 1.34 | -1.34 | 9.00 | |
| 0.67 | -2.67 | 9.00 | |
| 0.41 | -4.41 | 9.00 |
The values of coefficients A, B, C, D and a, b, C for the multiple depressions in fig. 6 (C) are shown in table 3, illustrating the effect of coefficient C, with the greater the absolute value of C, the greater the depth of the depression opening. By combining the example 3, it can be known that the coefficient C can realize free regulation and control of the concave vertex, and further realize control of the bending direction of the photon hook. Therefore, the concave shape of the concave micro-column can be changed by adjusting the coefficient of the structural constraint function, so that the regulation and control of the photon hook are realized.
TABLE 3
| A | B | C | D |
| 5 | -2 | -9 | -0.22 |
| 5 | -2 | -7.5 | -0.27 |
| 5 | -2 | -6 | -0.33 |
| 5 | -2 | -4.5 | -0.44 |
| 5 | -2 | -3 | -0.67 |
| a | b | c | |
| 1.56 | -1.16 | 9.00 | |
| 1.44 | -1.04 | 7.50 | |
| 1.31 | -0.91 | 6.00 | |
| 1.17 | -0.77 | 4.50 | |
| 1.00 | -0.60 | 3.00 |
How this embodiment implements coefficient setting follows the following steps:
from equations (2) to (5), the relationship between the coefficients can be found as follows:
B＝-A(a-b) (6)
-C＝Aab (7)
D＝-B/C (8)
the value range of the coefficient C is limited by the coordinate system setting and the radius of the micro-cylinder, in this embodiment, the value range of the coefficient C is (-10.43, -1.57), and finally determined as C = -9.00. Since the range of a and b is (0.25,5.00), the range of a obtained from equation (7) is (0.36, 144.00), and in this embodiment, a =2 is defined. According to the formula (6), the value range of B is (-9.50,9.50), which is determined as B =3.00 in this embodiment. Finally, based on equation (8), coefficient D =0.33 is obtained. Thus, the two-dimensional light field results under the above parameter settings are shown in fig. 7 (a), the effective length of the photon hook is 7.55 λ, and the bending angle is 17 °. If photon hooks of different lengths and bending angles are required, multiple sets of parameters and light field distribution results can be obtained by performing the above calculation steps. For example, as shown in fig. 7 (b), the photon hook bent to the right has good properties, wherein the effective length is L =8.72 λ, and the bending angle is α =15 °; as also shown in fig. 7 (c), this set of parameters achieves a leftward curved photonic hook of effective length L =5.96 λ and a bend angle α = -14 °; and as shown in fig. 7 (D), when the parameter sets a =1.44, B =2.28, C = -9.00, and D =0.25, a three-bend photon hook whose total effective length almost reaches 11.90 λ can be obtained.
Therefore, in the embodiment, the effective control of the characteristic parameters of the photon hook, such as longer or shorter effective length, different bending directions and various bending characteristics, is realized by adjusting the function coefficients, and a new method is provided for the regulation and control of the photon hook in general.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make various changes, modifications, additions and substitutions within the spirit and scope of the present invention.
Claims (4)
1. A method for generating a controllable photon hook by an irregular micro-nano structure is characterized by comprising the following steps:
s1, introducing a structural constraint function to describe an irregular part of the cross section of an irregular micro-nano structure, wherein the structural constraint function expression comprises n coefficients, and the irregular part is provided with m vertexes;
s2, determining coordinate information of the m vertexes in a rectangular plane coordinate system, and solving a relational expression between the abscissa or ordinate of the m vertexes and the n coefficients;
and S3, regulating and controlling the n coefficients by adjusting the abscissa or the ordinate of the m vertexes, so that the parameters of the photon hook are controlled.
2. The method according to claim 1, wherein the irregular micro-nano structure is a micro-nano structure with an arc-shaped recess in a cross section, the arc-shaped recess is described by a structural constraint function, the structural constraint function is an asymmetric parabolic-like function, and an expression is as follows:
x＝Ay 2 +By+C+Dxy (1)
wherein A, B, C, D is a coefficient of the structural constraint function;
let M, N, P denote three vertexes of the depression, and establish a plane rectangular coordinate system xoy with one point on the connecting line of MN as an origin O, and the intersection point of the depression and the x axis is P; m, N, P coordinates are (0,a), (0, -b), and (-c, 0), respectively, a, b, c are greater than 0;
and obtaining a relational expression between a, b and c and coefficients A, B and C, D, and regulating and controlling the coefficient A, B, C, D by adjusting the sizes of a, b and c.
3. The method for producing the adjustable photon hook by the irregular micro-nano structure according to claim 2, wherein the relation among a, b and c and coefficients A, B and C, D is as follows:
C＝-c (4)
4. the method for generating the adjustable photon hook according to the irregular micro-nano structure of claim 1, wherein the parameters of the photon hook comprise a bending angle, a bending direction and an effective length.
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| CN113066523A (en) * | 2021-04-16 | 2021-07-02 | 上海交通大学 | Lepidoptera micro-nano structure unified characterization method and system based on space trigonometric function |
| CN113552718A (en) * | 2021-07-26 | 2021-10-26 | 南开大学 | Micro-nano structure processing method and system |
| CN113900262A (en) * | 2021-11-15 | 2022-01-07 | 北京理工大学 | Generalized vortex beam-based metamaterial surface design method and preparation method |
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|---|---|---|---|---|
| CN110441834A (en) * | 2018-06-07 | 2019-11-12 | 华东师范大学 | The control method and control device of three dimensional photonic crystal lattice period and queueing discipline |
| CN113066523A (en) * | 2021-04-16 | 2021-07-02 | 上海交通大学 | Lepidoptera micro-nano structure unified characterization method and system based on space trigonometric function |
| CN113552718A (en) * | 2021-07-26 | 2021-10-26 | 南开大学 | Micro-nano structure processing method and system |
| CN113900262A (en) * | 2021-11-15 | 2022-01-07 | 北京理工大学 | Generalized vortex beam-based metamaterial surface design method and preparation method |
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